'Which is NOT' misread sprint

Answer the opposite of what a NOT/EXCEPT/LEAST question asks.

An error-pattern drill: practice spotting and avoiding this specific SHSAT trap.

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How to avoid misreading NOT and EXCEPT questions

Some questions ask for the one choice that does not fit. Example: which number is NOT a multiple of 3: 51, 72, 85, or 96? You check 51, see \(3 \times 17 = 51\), and pick it. But that is the opposite of what the question asks. The answer is 85, the only one that fails (\(8 + 5 = 13\), which is not a multiple of 3).

This trap catches strong students. Your brain is trained to look for the choice that works, and here three of the four choices work. The math is easy; the reading is the hard part.

Check habits:

Worked examples

Example 1.
Which of the following is NOT divisible by 9: 705, 963, 576, or 774?
Show answer and explanation
Answer:
C

705 has a digit sum of 12, a multiple of 3 but not of 9, so 705 \(\div\) 9 leaves a remainder of 3. The other choices are divisible: \(963 = 9 \times 107\), \(576 = 9 \times 64\), \(774 = 9 \times 86\). (Choosing one of them answers which number IS divisible.)

Example 2.
The ratio of blue paint cans to white paint cans is 4:9. Which of the following ratios is NOT equivalent to this ratio?
Show answer and explanation
Answer:
A

An equivalent ratio multiplies both terms of 4:9 by the same number: 12:27 is \(4 \times 3 : 9 \times 3\); 24:54 is \(4 \times 6 : 9 \times 6\); 28:63 is \(4 \times 7 : 9 \times 7\). But 8:13 adds 4 to both terms, and adding does not keep the ratio the same, so it is NOT equivalent. (Choosing 12:27, 24:54 or 28:63 means the word NOT was missed.)

Example 3.
5 friends, including Ben and Eli, stand in a line. In how many arrangements are Ben and Eli NOT next to each other?
Show answer and explanation
Answer:
D

Count the opposite and subtract. All arrangements: \(5! = 120\). Together: glue Ben and Eli into one block, so arrange 4 items in \(4! = 24\) ways, times 2 for the order inside the block: \(48\). Not together: \(120 - 48 = 72\). (Counting the arrangements where they ARE next to each other gives 48. Forgetting that Ben and Eli can switch places in the block (\(120 - 24\)) gives 96. Ignoring the condition (\(5!\)) gives 120.)